Abstract Convex Underestimation Assisted Multistage Differential Evolution
提出一种利用抽象凸下界估计来划分进化阶段的多阶段差分进化算法，根据平均下界误差自动切换策略，并设计基于质心的策略以平衡种群多样性与收敛速度，在多个基准测试上表现优于现有方法。
In differential evolution (DE), different strategies applied in different evolutionary stages may be more effective than a single strategy used in the entire evolutionary process. However, it is not trivial to appropriately determine the evolutionary stage. In this paper, we present an abstract convex underestimation-assisted multistage DE. In the proposed algorithm, the underestimation is calculated through the supporting vectors of some neighboring individuals. Based on the variation of the average underestimation error (UE), the evolutionary process is divided into three stages. Each stage includes a pool of suitable candidate strategies. At the beginning of each generation, the evolutionary stage is first estimated according to the average UE of the previous generation. Subsequently, a strategy is automatically chosen from the corresponding candidate pool to create a mutant vector. In addition, a centroid-based strategy which utilizes the information of multiple superior individuals is designed to balance the population diversity and convergence speed in the second stage. Experiments are conducted on 23 widely used test functions, CEC 2013, and CEC 2014 benchmark sets to demonstrate the performance of the proposed algorithm. The results reveal that the proposed algorithm exhibits better performance compared with several advanced DE variants and some non-DE approaches.